S = \(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{17x19}\)
2S = \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\)\(\frac{1}{17}-\frac{1}{19}\)
2S = \(\frac{1}{3}-\frac{1}{19}\)
2S = \(\frac{16}{57}\)
S = \(\frac{16}{57}\times\frac{1}{2}\)
S = \(\frac{8}{57}\)
\(S=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}+\frac{1}{255}+\frac{1}{323}\)
\(S=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+\frac{1}{15\cdot17}+\frac{1}{17\cdot19}\)
\(2S=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{15\cdot17}+\frac{2}{17\cdot19}\)
\(2S=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}\)
\(2S=\frac{1}{3}-\frac{1}{19}\)
\(2S=\frac{19}{57}-\frac{3}{57}\)
\(2S=\frac{16}{57}\)
\(S=\frac{16}{57}:2\)
\(S=\frac{16}{57}\cdot\frac{1}{2}\)
\(S=\frac{8}{57}\)
Ta có: S = 1/15 + 1/35 + 1/63 +...+1/323
=>S = 1/3.5 + 1/5.7 + 1/7.9 +...+ 1/17.19
=>S = 1/2(2/3.5 + 2/5.7 + 2/7.9 +...+ 2/17.19)
=>S = 1/2(1/3 - 1/5 + 1/5 - 1/7 + 1/7 -1/9 +...+ 1/17 - 1/19)
=>S = 1/2(1/3 - 1/19)
=>S = 1/2 . 16/57
=>S = 8/57.
ko viết lạ đề
\(S=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{17.19}\)
=\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\)
=\(\frac{1}{3}-\frac{1}{19}=\frac{16}{57}\)
quy luật nè:
15=3.5
35=5.7
63=7.9
99=9.11
143=11.13
195=13.15
255=15.17
323=17.19
bạn tự làm tiếp nha
chúc bạn học tốt
